Abstract: Aiming at the defects of dynamic system prediction model such as low modeling efficiency and lack of explicit models, a High Order Ordinary Differential Equations Model based on GEP（GEP-HODE） has been proposed in this passage. In the first place, higher order differentials are used to express the change characteristics of one-dimensional data and an explicit model is gotten by modeling the high-order differential data using GEP. Then, this paper reduces the order of HODE model and uses numerical methods to obtain the predicted values. This method utilizes the coding characteristics of the “genotype-phenotype” of the GEP, achieving synchronization of modeling and parameter optimization, and greatly improving modeling efficiency. Yearly mean sunspots number are used to model and predict. The results show that this method has more efficiency of model compared with GP hybrid method and more accuracy compared with other predict models like hybrid BP neural network model.

Key words: gene expression programming, dynamic system modeling, high order differential equation model, time series prediction

摘要： 针对动态系统预测建模中建模效率低，无显式模型的缺陷。提出一种基于基因表达式编程（GEP）的高阶常微分方程预测模型（GEP-HODE）。将一维数据的变化特性使用高阶微分进行表示，通过GEP对高阶微分数据进行建模，得到显式模型。对高阶常微分方程模型进行降阶处理，使用数值方法进行求解，得到预测值。该方法利用了GEP算法“基因型-表现型”的编码特性，实现了模型建立与参数优化的同步，大幅度提升建模效率。以太阳黑子年平均数作为实验数据建模预测，结果表明，该方法相比GP混合建模方法有更高的效率，相比混合BP神经网络模型等方法有更好的精度。

关键词: 基因表达式编程, 动态系统建模, 高阶常微分方程模型, 时间序列预测